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He is listed as an ISI highly cited researcher in mathematics, [2] is the most cited author in the journal Numerical Linear Algebra with Applications, [3] [4] and is the author of the highly cited book Iterative Methods for Sparse Linear Systems. He is a SIAM fellow (class of 2010) and a fellow of the AAAS (2011).
With respect to general linear maps, linear endomorphisms and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other part of mathematics.
In mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, category theory, and algebraic geometry. A semi-simple object is one that can be decomposed into a sum of simple objects, and simple objects are those that do not contain non-trivial proper sub-objects. The ...
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
Symmetric polynomials are important to linear algebra, representation theory, and Galois theory. They are also important in combinatorics, where they are mostly studied through the ring of symmetric functions, which avoids having to carry around a fixed number of variables all the time.
In mathematics, specifically linear algebra, the Woodbury matrix identity – named after Max A. Woodbury [1] [2] – says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix.
The representations of the group are found by considering representations of (), the Lie algebra of SU(2).Since the group SU(2) is simply connected, every representation of its Lie algebra can be integrated to a group representation; [1] we will give an explicit construction of the representations at the group level below.
In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [1] [2] It is occasionally known as adjunct matrix, [3] [4] or "adjoint", [5] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
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